Macroeconomics & Sustainable Development
Hartwick Rule & Genuine Saving (ANS) Formula
Calculate World Bank Adjusted Net Saving GNS - D_cap + E_edu - R_dep - D_pol and test John Hartwick’s (1977) wealth-sustainability reinvestment rule.
Spot phantom GDP booms when resource depletion exceeds physical and human-capital investment!
Conventional national accounts treat pumping oil, mining copper, and clearing timber solely as positive GDP income without deducting natural-capital depletion! John Hartwick (1977) proved that an exhaustible-resource economy sustains non-declining per-capita consumption ONLY if 100% of scarcity rents are reinvested into reproducible physical and human capital. Operationalized by Kirk Hamilton and the World Bank as Adjusted Net Saving (Genuine Saving), ANS = GNS - D_cap + E_edu - R_dep - D_pol starts from Gross National Saving GNS, subtracts produced-capital depreciation D_cap, ADDS public education human-capital investment E_edu, and SUBTRACTS natural-resource depletion R_dep plus pollution/carbon health damages D_pol!
Check by hand on Gross_Saving_GNS = 240 (B2), Capital_Depreciation_Dcap = 110 (B3), Education_Investment_Eedu = 45 (B4), Resource_Depletion_Rdep = 150 (B5), Pollution_Damage_Dpol = 40 (B6), and Gross_National_Income_GNI = 1,000 (B7): headline Net National Saving looks buoyant at 240 - 110 = +130.00 (+13.00% of GNI), yet Genuine Saving is 130 + 45 - 150 - 40 = -15.00 (-0.0150 = -1.50% of GNI!), exposing unsustainable wealth liquidation (Hartwick Reinvestment Ratio 175 / 190 = 0.9211 < 1.00)!
| National Wealth Accounting Line (GNI = 1,000) | Formula | Verified Output |
|---|---|---|
| Conventional Net National Saving (NNS) | GNS - D_cap | +130.00 (+13.00% of GNI) |
| Human-Capital Adjusted Saving | GNS - D_cap + E_edu | +175.00 |
| Genuine Saving / Adjusted Net Saving (ANS) | GNS - D_cap + E_edu - R_dep - D_pol | -15.00 (Wealth Declining!) |
| Genuine Saving Share of GNI | ANS / GNI | -0.0150 (-1.50% of GNI) |
World Bank Genuine Saving (Adjusted Net Saving) Formula
Validate non-negative depreciation, education, depletion, and pollution lines plus positive GNI.
=LET(g_sv, B2, d_cp, B3, e_ed, B4, r_dp, B5, d_pl, B6, g_ni, B7, IF(OR(d_cp < 0, e_ed < 0, r_dp < 0, d_pl < 0, g_ni <= 0), "Invalid Wealth Account Input", ROUND(g_sv - d_cp + e_ed - r_dp - d_pl, 2)))Genuine Saving Rate (% of GNI) & Hartwick Sustainability Test Formula
Test raising Sovereign Wealth / Gross Saving GNS from 240 to 275: Genuine Saving flips from -15.00 to +20.00 (+0.0200 of GNI), satisfying Hartwick’s Rule!
=IF(ISTEXT(E3), E3, ROUND(E3 / B7, 4))Try the example
Use the original values or change them to test your understanding.